IJPAM: Volume 81, No. 1 (2012)

Abstract. Let
be a fixed subset of nonnegative integers and let ,
be given complex numbers. We consider a free unital associative complex algebra generated by generators
(each of degree one) together with linear operators
,
that act as twisted derivations on . The algebra is graded by total degree. More generally could be considered as multigraded. Then it has a direct sum decomposition into multigraded (weight) subspaces
, where runs over multisets (over ).
An element in is called a constant if it is annihilated by all operators
.
Then the fundamental problem is to describe the space of all constants in algebra . The space also inherits the direct sum decomposition into multigraded subspaces
. Thus it is enough to determine the finite dimensional spaces
.